Abstract
Manfred R. Schroeder made influential contributions to acoustics by applying number theory. He introduced number-theory sequences in room impulse response measurements, applied number-theoretical sequences to shape wall surfaces for diffuse sound reflections. Another area Manfred Schroeder made broad impact is invention of an artificial reverberator using all-pass transfer- function properties to create colorless reverberation using a simple algorithm. Vast research activities and engineering developments over past decades have extended Schroeder’s work involving artificial reverberators, artificial stereo and applications of maximum-length sequences. This chapter briefs a number of recent applications of maximum-length and quadratic-residue sequences, such as simultaneous dual/multiple sources measurements in acoustical tomography, in artificial pseudo-binaural reverberation, in decorrelation for spatial audio signals, and room acoustic diffuser design.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Schroeder, M.R.: Improved quasi-stereophony and “Colorless” artificial reverberation. J. Acoust. Soc. Am. 33, 1061–1064 (1961)
Schroeder, M.R.: Colorless artificial reverberation. J. Audio Eng. Soc. 9, 192–197 (1961)
Schroeder, M.R.: Diffuse sound reflection by maximum-length sequences. J. Acoust. Soc. Am. 57, 149–150 (1975)
Schroeder, M.R.: Integrated-impulse method measuring sound decay without using impulses. J. Acoust. Soc. Am. 66, 497–500 (1979)
Schroeder, M.R.: Binaural dissimilarity and optimum ceilings for concert halls: more lateral sound diffusion. J. Acoust. Soc. Am. 65, 958–963 (1979)
Cox, T.J., D’Antonio, P.: Acoustic Absorbers and Diffusers, 2nd edn. Taylor & Francis, London (2009)
Schroeder, M.R.: Number Theory in Science and Communication. Springer, Berlin (1991). 2nd enl. edn
Xiang, N.: Digital sequences. In: Havelock, D., Kuwano, S., Vorländer, M., et al. (eds.) Handbook of Signal Processing in Acoustics, pp. 87–106. Springer, Berlin (2008)
Xiang, N., Genuit, K.: Characteristic maximum-length sequences for the interleaved sampling method. Acustica 82, 905–907 (1996)
Xiang, N., Schroeder, M.R.: Reciprocal maximum-length sequence pairs for acoustical dual source measurements. J. Acoust. Soc. Am. 113, 2754–2761 (2003)
Xiang, N., Daigle, J.N., Kleiner, M.: Simultaneous acoustic channel measurement via maximal-length-related sequences. J. Acoust. Soc. Am. 117, 1889–1894 (2005)
Ziemann, A., Arnold, K., Raabe, A.: Acoustic tomography as a method to identify small-scale land surface characteristics. Acta Acust. Acust. 87, 731–737 (2001)
Xiang, N., Li, S.: A pseudo-inverse algorithm for simultaneous measurements using multiple acoustical sources (L). J. Acoust. Soc. Am. 121, 1299–1302 (2007)
Gardner, W.C.: Reverberation Algorithms. Kluwer Academic Publishers, Dordrecht (1998)
Blesser, B.: An interdisciplinary synthesis of reverberation viewpoints. J. Audio Eng. Soc. 49, 867–903 (2001)
Moorer, J.: About this reverberation business. Comput. Music J. 3, 13–28 (1979)
Gardner, W.G.: Efficient convolution without input-output delay. J. Audio Eng. Soc. 43, 127–136 (1995)
Van Maercke, D., Martin, J., Vian, J.-P.: Binaural simulation of concert halls: a new approach for the binaural reverberation process. J. Acoust. Soc. Am. 94, 3255–3264 (1993)
Olson, S.: Understanding the perception of double-sloped energy decays: a multidimensional scaling approach. M.S. thesis, School of Architecture, Rensselaer Polytechnic Institute (2008)
Blauert, J.: Spatial Hearing. MIT Press, Cambridge, MA (2001)
Trivedi, U., Dieckman, E., Xiang, N.: Reciprocal maximum-length and related sequences for artificial spatial enveloping reverberation (A). J. Acoust. Soc. Am. 125, 2735 (2009)
Trivedi, U., Xiang, N.: Utilizing reciprocal maximum length sequences within a multichannel context to generate a natural, spatial sounding reverberation (A). J. Acoust. Soc. Am. 126, 2155 (2009)
Xie, B.-S., Shi, B., Xiang, N.: Audio signal decorrelation based on reciprocal maximal-length sequence filters and its applications to spatial sound. Preprint 8805, the 133rd convention of the Audio Eng. Soc., San Francisco, CA, 2012
Kendall, G.S.: The decorrelation of audio signals and its impact on spatial imagery. Comput. Music J. 19, 71 (1995)
Daigle, J.N., Xiang, N.: A specialized cross-correlation algorithm for acoustical measurements using coded sequences. J. Acoust. Soc. Am. 119, 330 (2006)
Beranek, L.: Concert Hall and Opera Houses, 2nd edn. Springer, New York (2004)
Schroeder, M.R.: Chaos, Power Laws: Minutes from an Infinite Paradise. W.H. Freeman & Co., San Francisco, CA (1991)
Fan, P., Darnell, M.: Sequence Design for Communications Applications. Wiley, New York (1996)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Xiang, N., Xie, B., Cox, T.J. (2015). Recent Applications of Number-Theoretic Sequences in Audio and Acoustics. In: Xiang, N., Sessler, G. (eds) Acoustics, Information, and Communication. Modern Acoustics and Signal Processing. Springer, Cham. https://doi.org/10.1007/978-3-319-05660-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-05660-9_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05659-3
Online ISBN: 978-3-319-05660-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)